3 Answers
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Going over the RAW, I can't find any limitation on the ability score. I checked in the D&D 3.5 SRD as well, but it looks like Pathfinder adapted that nearly word-for-word, and I couldn't find any limitation there either. Don't forget, though, that they won't stack, of course. Once you find a pair of good +2 Dexterity gloves, your little puny belt will be useless - and you might regret not putting that ability point into Dexterity then. :)

However, I can think of one very good reason why a DM might not allow them:

They leak the mechanics into the game world. The breaking down of abilities into discrete steps is a system choice that doesn't translate into the character's world. The fact that it takes two steps to improve a bonus doesn't change the fact that for the characters, their dexterity lies on a vague spectrum of ability. Given that, it would be strange for a wizard to enchant an item that makes one person noticeably stronger (the one with the odd ability score), while the same magic does nothing for another who is just as strong, for most purposes, but whose out-of-character score is one lower. Especially since at an equally arbitrary point in time for that person (say... level 4?) the magic item might suddenly start working.

One can work with that, in-setting, of course. You can tie the ability score steps to various in-universe mystical parameters. But that's opening a can of worms, where one aspect of the system is mapped into an in-universe factor, others will be dragged in as well, and you'll be forced into rationalizing every single bit of system mechanics, which will not end well.

For that reason alone, I can understand a DM who will rule out odd-numbered stat-bonus items. They leak the abstraction.

Would an item that grants a +1 bonus only to a given ability score require a lower caster level than those that add +2?

You shouldn't have things that grant a "+ odd number" to an ability score. The reason for this is that a +2 or +4 always means something (your bonus increases to a +1 or a +2 no matter what your score). A "+ odd number" only means something if you have an odd score. Not only is that weird ("This belt makes me stronger when I wear it, but not you."), it also makes it too tempting to min-max with such an item.

By the letter, you are golden. However, using even bonuses guarantees a modifier no matter what the score is. However looking at the exponential cost and therefore time necessary to create it, a cheap little cantrip level trinket should be a pittance in the eyes of your DM, who has ultimate decision on the minimum magic needed.